论文标题
关于对具有较小编成代数的小代数分类的问题
On the problem of classifying solvable Lie algebras having small codimensional derived algebras
论文作者
论文摘要
This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of $n$-dimensional nilpotent Lie algebras is given.另一方面，对所有$（n+2）$ - 具有2个二维派生代数的代数分类的问题被证明是狂野的。在这种情况下，我们提供了一种分类所考虑的谎言代数的子类的方法，该子类通过包含至少一个内部衍生的一对派生从其派生的代数延伸。
This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of $n$-dimensional nilpotent Lie algebras is given. On the other hand, the problem of classifying all $(n+2)$-dimensional real solvable Lie algebras having 2-codimensional derived algebras is proved to be wild. In this case, we provide a method to classify a subclass of the considered Lie algebras which are extended from their derived algebras by a pair of derivations containing at least one inner derivation.
